We see that most real data do not share the properties of Brownian motion. | ||||
The comparisons are clearest when we view differences instead of the raw data. | ||||
Here are difference graphs for two examples of Brownian motion. | ||||
For comparison, below these are difference graphs for four years of EMC closing prices (left) and Dell closing prices (right). | ||||
For later reference we note that when the thickness of the plotting line is approximately equal to the spacing between successive values, the bulk of the difference plot merges into a band. | ||||
Further, for Brownian motion (top two graphs) we observe | ||||
  1. The band is of approximately constant width. | ||||
  2. The outliers are relatively small (this is called the short tails property). | ||||
  3. The outliers are approximately uniformly distributed. | ||||
How well do real data satisfy these conditions? At least for EMC and Dell, the match appears to be weak. |
Return to Brownian Motion.